Search results for: Spectral Analysis.

Authors: J. P. Dubois

Abstract:

Pulse code modulation is a widespread technique in digital communication with significant impact on existing modern and proposed future communication technologies. Its widespread utilization is due to its simplicity and attractive spectral characteristics. In this paper, we present a new approach to the spectral analysis of PCM signals using Riemann-Stieltjes integrals, which is very accurate for high bit rates. This approach can serve as a model for similar spectral analysis of other competing modulation schemes.

Keywords: Coding, discrete Fourier, power spectral density, pulse code modulation, Riemann-Stieltjes integrals.

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Authors: Kui Du

Abstract:

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions.

Keywords: Spectral norm, Numerical radius, Spectral radius, Ratios

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Authors: Martin De Biasio, Raimund Leitner, Franz G. Wuertz, Sergey Verzakov, Pierre J. Elbischger

Abstract:

Breast carcinoma is the most common form of cancer in women. Multicolour fluorescent in-situ hybridisation (m-FISH) is a common method for staging breast carcinoma. The interpretation of m-FISH images is complicated due to two effects: (i) Spectral overlap in the emission spectra of fluorochrome marked DNA probes and (ii) tissue autofluorescence. In this paper hyper-spectral images of m-FISH samples are used and spectral unmixing is applied to produce false colour images with higher contrast and better information content than standard RGB images. The spectral unmixing is realised by combinations of: Orthogonal Projection Analysis (OPA), Alterating Least Squares (ALS), Simple-to-use Interactive Self-Modeling Mixture Analysis (SIMPLISMA) and VARIMAX. These are applied on the data to reduce tissue autofluorescence and resolve the spectral overlap in the emission spectra. The results show that spectral unmixing methods reduce the intensity caused by tissue autofluorescence by up to 78% and enhance image contrast by algorithmically reducing the overlap of the emission spectra.

Keywords: breast carcinoma, hyperspectral imaging, m-FISH, spectral unmixing

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Authors: Liping Li, Changchun Liu, Ke Li, Chengyu Liu

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Non-stationary trend in R-R interval series is considered as a main factor that could highly influence the evaluation of spectral analysis. It is suggested to remove trends in order to obtain reliable results. In this study, three detrending methods, the smoothness prior approach, the wavelet and the empirical mode decomposition, were compared on artificial R-R interval series with four types of simulated trends. The Lomb-Scargle periodogram was used for spectral analysis of R-R interval series. Results indicated that the wavelet method showed a better overall performance than the other two methods, and more time-saving, too. Therefore it was selected for spectral analysis of real R-R interval series of thirty-seven healthy subjects. Significant decreases (19.94±5.87% in the low frequency band and 18.97±5.78% in the ratio (p<0.001)) were found. Thus the wavelet method is recommended as an optimal choice for use.

Keywords: empirical mode decomposition, heart rate variability, signal detrending, smoothness priors, wavelet

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Authors: O. J. G. Somsen

Abstract:

One of the tasks of optical surveillance is to detect anomalies in large amounts of image data. However, if the size of the anomaly is very small, limited information is available to distinguish it from the surrounding environment. Spectral detection provides a useful source of additional information and may help to detect anomalies with a size of a few pixels or less. Unfortunately, spectral cameras are expensive because of the difficulty of separating two spatial in addition to one spectral dimension. We investigate the possibility of modifying a simple spectral line detector for outdoor detection. This may be especially useful if the area of interest forms a line, such as the horizon. We use a monochrome CCD that also enables detection into the near infrared. A simple camera is attached to the setup to determine which part of the environment is spectrally imaged. Our preliminary results indicate that sensitive detection of very small targets is indeed possible. Spectra could be taken from the various targets by averaging columns in the line image. By imaging a set of lines of various widths we found narrow lines that could not be seen in the color image but remained visible in the spectral line image. A simultaneous analysis of the entire spectra can produce better results than visual inspection of the line spectral image. We are presently developing calibration targets for spatial and spectral focusing and alignment with the spatial camera. This will present improved results and more use in outdoor application.

Keywords: Anomaly detection, spectroscopic line imaging, image analysis.

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Authors: Abdulhamit Donder, Erhan Ilhan Konukseven

Abstract:

Grinding operation is performed in order to obtain desired surfaces precisely in machining process. The needed relative motion between the cutting tool and the workpiece is generally created either by the movement of the cutting tool or by the movement of the workpiece or by the movement of both of them as in our case. For all these cases, the coherence level between the movements and the interaction forces is a key influential parameter for efficient grinding. Therefore, in this work, spectral coherence analysis has been performed to investigate the coherence level between grinding interaction forces and the movement of the workpiece on our robotic-grinding experimental setup in METU Mechatronics Laboratory.

Keywords: Coherence analysis, correlation, FFT, grinding, Hanning window, machining, Piezo actuator, reverse arrangements test, spectral analysis.

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Authors: Keunseok Cho, Sangbae Jeong, Hyungwook Chang, Minsoo Hahn

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In this paper, a new encoding algorithm of spectral envelope based on NLMS in G.729.1 for VoIP is proposed. In the TDAC part of G.729.1, the spectral envelope and MDCT coefficients extracted in the weighted CELP coding error (lower-band) and the higher-band input signal are encoded. In order to reduce allocation bits for spectral envelope coding, a new quantization algorithm based on NLMS is proposed. Also, reduced bits are used to enhance sound quality. The performance of the proposed algorithm is evaluated by sound quality and bit reduction rates in clean and frame loss conditions.

Keywords: G.729.1, MDCT coefficient, NLMS, spectral envelope.

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

Abstract:

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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Authors: Mst Ilme Faridatul, Bo Wu

Abstract:

Multi-temporal urban land cover mapping is of paramount importance for monitoring urban sprawl and managing the ecological environment. For diversified urban activities, it is challenging to map land covers in a complex urban environment. Spectral indices have proved to be effective for mapping urban land covers. To improve multi-temporal urban land cover classification and mapping, we evaluate the performance of three spectral indices, e.g. modified normalized difference bare-land index (MNDBI), tasseled cap water and vegetation index (TCWVI) and shadow index (ShDI). The MNDBI is developed to evaluate its performance of enhancing urban impervious areas by separating bare lands. A tasseled cap index, TCWVI is developed to evaluate its competence to detect vegetation and water simultaneously. The ShDI is developed to maximize the spectral difference between shadows of skyscrapers and water and enhance water detection. First, this paper presents a comparative analysis of three spectral indices using Landsat Enhanced Thematic Mapper (ETM), Thematic Mapper (TM) and Operational Land Imager (OLI) data. Second, optimized thresholds of the spectral indices are imputed to classify land covers, and finally, their performance of enhancing multi-temporal urban land cover mapping is assessed. The results indicate that the spectral indices are competent to enhance multi-temporal urban land cover mapping and achieves an overall classification accuracy of 93-96%.

Keywords: Land cover, mapping, multi-temporal, spectral indices.

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Authors: Kaveh Shahi, Helmi Z. M. Shafri, Ebrahim Taherzadeh

Abstract:

In remote sensing, shadow causes problems in many applications such as change detection and classification. It is caused by objects which are elevated, thus can directly affect the accuracy of information. For these reasons, it is very important to detect shadows particularly in urban high spatial resolution imagery which created a significant problem. This paper focuses on automatic shadow detection based on a new spectral index for multispectral imagery known as Shadow Detection Index (SDI). The new spectral index was tested on different areas of WorldView-2 images and the results demonstrated that the new spectral index has a massive potential to extract shadows with accuracy of 94% effectively and automatically. Furthermore, the new shadow detection index improved road extraction from 82% to 93%.

Keywords: Spectral index, shadow detection, remote sensing images, WorldView-2.

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Authors: A. Manallah, C. Meier

Abstract:

Confocal spectral interferometry (CSI) is an innovative optical method for determining microtopography of surfaces and thickness of transparent layers, based on the combination of two optical principles: confocal imaging, and spectral interferometry. Confocal optical system images at each instant a single point of the sample. The whole surface is reconstructed by plan scanning. The interference signal generated by mixing two white-light beams is analyzed using a spectrometer. In this work, five ‘rugotests’ of known standard roughnesses are investigated. The topography is then measured and illustrated, and the equivalent roughness is determined and compared with the standard values.

Keywords: Confocal spectral interferometry, Nondestructive testing, Optical metrology, Surface topography, Roughness.

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.

Keywords: Power Spectral Density (PSD), quasi-stationarytime series, short time Fourier Transform, Sliding window DFT.

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Authors: Mohamad Reza. Mohaghegh, Majid. Malek Jafarian

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This research proposes an algorithm for the simulation of time-periodic unsteady problems via the solution unsteady Euler and Navier-Stokes equations. This algorithm which is called Time Spectral method uses a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. It has shown tremendous potential for reducing the computational cost compared to conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy. The accuracy and efficiency of this technique is verified by Euler and Navier-Stokes calculations for pitching airfoils. Because of flow turbulence nature, Baldwin-Lomax turbulence model has been used at viscous flow analysis. The results presented by the Time Spectral method are compared with experimental data. It has shown tremendous potential for reducing the computational cost compared to the conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy, because results verify the small number of time intervals per pitching cycle required to capture the flow physics.

Keywords: Time Spectral Method, Time-periodic unsteadyflow, Discrete Fourier transform, Pitching airfoil, Turbulence flow

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Authors: P. Sophon, M. Kruachanta, S. Chaisri, G. Leaungvongpaisan, P. Wongpornchai

Abstract:

The thick bed hydrocarbon reservoirs are primarily interested because of the more prolific production. When the amount of petroleum in the thick bed starts decreasing, the thin bed reservoirs are the alternative targets to maintain the reserves. The conventional interpretation of seismic data cannot delineate the thin bed having thickness less than the vertical seismic resolution. Therefore, spectral decomposition and instantaneous seismic attributes were used to delineate the thin bed in this study. Short Window Discrete Fourier Transform (SWDFT) spectral decomposition and instantaneous frequency attributes were used to reveal the thin bed reservoir, while Continuous Wavelet Transform (CWT) spectral decomposition and envelope (instantaneous amplitude) attributes were used to indicate hydrocarbon bearing zone. The study area is located in the Pohokura Field, Taranaki Basin, New Zealand. The thin bed target is the uppermost part of Mangahewa Formation, the most productive in the gas-condensate production in the Pohokura Field. According to the time-frequency analysis, SWDFT spectral decomposition can reveal the thin bed using a 72 Hz SWDFT isofrequency section and map, and that is confirmed by the instantaneous frequency attribute. The envelope attribute showing the high anomaly indicates the hydrocarbon accumulation area at the thin bed target. Moreover, the CWT spectral decomposition shows the low-frequency shadow zone and abnormal seismic attenuation in the higher isofrequencies below the thin bed confirms that the thin bed can be a prospective hydrocarbon zone.

Keywords: Hydrocarbon indication, instantaneous seismic attribute, spectral decomposition, thin bed delineation.

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Authors: Özlen Altun, Zeliha Yoruç

Abstract:

In the present study, the reactions involving 4-bromo-2,6-bis-hydroxymethyl-phenol (BBHMP) and nicotinamide (NA) in the presence of Pd(II) ions were investigated. Optimum conditions for the reactions were established as pH = 7 and λ = 450 nm. According to absorbance measurements, the molar ratio of BBHMP: NA: Pd²⁺ was found to be 1: 2: 2. As a result of physicochemical, spectrophotometric and thermal analyses, the reactions of BBHMP and NA with Pd(II) are complexation reactions and one molecule of BBHMP and two molecules of NA react with two molecules of the Pd(II) ion.

Keywords: Nicotinamide, 4-bromo-2, 6-bis-hydroxymethyl-phenol, Pd(II), spectral analysis, synthesis.

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Authors: Guangbin Wang, Xue Li, Fuping Tan

Abstract:

In this paper, we present some new upper bounds for the spectral radius of iterative matrices based on the concept of doubly α diagonally dominant matrix. And subsequently, we give two examples to show that our results are better than the earlier ones.

Keywords: doubly α diagonally dominant matrix, eigenvalue, iterative matrix, spectral radius, upper bound.

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Authors: Talbi Mourad, Salhi Lotfi, Chérif Adnen

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In this work, we are interested in developing a speech denoising tool by using a discrete wavelet packet transform (DWPT). This speech denoising tool will be employed for applications of recognition, coding and synthesis. For noise reduction, instead of applying the classical thresholding technique, some wavelet packet nodes are set to zero and the others are thresholded. To estimate the non stationary noise level, we employ the spectral entropy. A comparison of our proposed technique to classical denoising methods based on thresholding and spectral subtraction is made in order to evaluate our approach. The experimental implementation uses speech signals corrupted by two sorts of noise, white and Volvo noises. The obtained results from listening tests show that our proposed technique is better than spectral subtraction. The obtained results from SNR computation show the superiority of our technique when compared to the classical thresholding method using the modified hard thresholding function based on u-law algorithm.

Keywords: Enhancement, spectral subtraction, SNR, discrete wavelet packet transform, spectral entropy Histogram

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Authors: C. Ganesh Babu, P. T. Vanathi

Abstract:

In this paper we present an enhanced noise reduction method for robust speech recognition using Adaptive Gain Equalizer with Non linear Spectral Subtraction. In Adaptive Gain Equalizer method (AGE), the input signal is divided into a number of subbands that are individually weighed in time domain, in accordance to the short time Signal-to-Noise Ratio (SNR) in each subband estimation at every time instant. Instead of focusing on suppression the noise on speech enhancement is focused. When analysis was done under various noise conditions for speech recognition, it was found that Adaptive Gain Equalizer method algorithm has an obvious failing point for a SNR of -5 dB, with inadequate levels of noise suppression for SNR less than this point. This work proposes the implementation of AGE when coupled with Non linear Spectral Subtraction (AGE-NSS) for robust speech recognition. The experimental result shows that out AGE-NSS performs the AGE when SNR drops below -5db level.

Keywords: Adaptive Gain Equalizer, Non Linear Spectral Subtraction, Speech Enhancement, and Speech Recognition.

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Authors: Yadan Mao, Chengwang Lei, John C. Patterson

Abstract:

The mixing of pollutions and sediments in near shore regions of natural water bodies depends heavily on the characteristics such as the strength and frequency of flow instability. In the present paper, the instability of natural convection induced by absorption of solar radiation in littoral regions is considered. Spectral analysis is conducted on the quasi-steady state flow to reveal the power and frequency modes of the instability at various positions. Results indicate that the power of instability, the number of frequency modes, the prominence of higher frequency modes, and the highest frequency mode increase with the offshore distance and/or Rayleigh number. Harmonic modes are present at relatively low Rayleigh numbers. For a given offshore distance, the position with the strongest power of instability is located adjacent to the sloping bottom while the frequency modes are the same over the local depth. As the Rayleigh number increases, the unstable region extends toward the shore.

Keywords: Instability, Littoral waters, natural convection, Spectral analysis

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Authors: Yue-Der Lin, Wei-Ting Liu, Ching-Che Tsai, Wen-Hsiu Chen

Abstract:

PPG is a potential tool in clinical applications. Among such, the relationship between respiration and PPG signal has attracted attention in past decades. In this research, a bivariate AR spectral estimation method was utilized for the coherence analysis between these two signals. Ten healthy subjects participated in this research with signals measured at different respiratory rates. The results demonstrate that high coherence exists between respiration and PPG signal, whereas the coherence disappears in breath-holding experiments. These results imply that PPG signal reveals the respiratory information. The utilized method may provide an attractive alternative approach for the related researches.

Keywords: Coherence analysis, photoplethysmography (PPG), bivariate AR spectral estimation.

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Authors: M. Amelsakhi, A. Sohrabi-Bidar, A. Shareghi

Abstract:

One of the most important issues about the structural damages caused by earthquake is the evaluating of the spectral response of the site on which the construction is built. This fact has demonstrated during many earlier earthquakes and many researchers’ reports have concerned with it. According to these reports, features of the site materials and geometry of the ground surface are considered the main factors. This study concentrates on the specific form of topographies like hills. Assessing of spectral responses of different points on the hills and beside demonstrates considerable differences between 1D and 2D methods of geotechnical analyses. A general trend of amplifications on the top of the hills and de-amplifications near the toe of the hills has been appeared within the acceleration, velocity and displacement response spectrums of horizontal motion. Evaluating of spectral responses of different sizes of the hills revealed that as much as the hill-size enlarges differences between spectral responses of 1D and 2D analyses transfers to longer range of periods and becomes wider.

Keywords: Topography effect, Amplification ratio, Response spectrum.

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Authors: Yongquan Zhao, Bo Huang

Abstract:

Spatial, Temporal, and Spectral Resolution (STSR) are three key characteristics of Earth observation satellite sensors; however, any single satellite sensor cannot provide Earth observations with high STSR simultaneously because of the hardware technology limitations of satellite sensors. On the other hand, a conflicting circumstance is that the demand for high STSR has been growing with the remote sensing application development. Although image fusion technology provides a feasible means to overcome the limitations of the current Earth observation data, the current fusion technologies cannot enhance all STSR simultaneously and provide high enough resolution improvement level. This study proposes a Hybrid Spatial-Temporal-Spectral image Fusion Model (HSTSFM) to generate synthetic satellite data with high STSR simultaneously, which blends the high spatial resolution from the panchromatic image of Landsat-8 Operational Land Imager (OLI), the high temporal resolution from the multi-spectral image of Moderate Resolution Imaging Spectroradiometer (MODIS), and the high spectral resolution from the hyper-spectral image of Hyperion to produce high STSR images. The proposed HSTSFM contains three fusion modules: (1) spatial-spectral image fusion; (2) spatial-temporal image fusion; (3) temporal-spectral image fusion. A set of test data with both phenological and land cover type changes in Beijing suburb area, China is adopted to demonstrate the performance of the proposed method. The experimental results indicate that HSTSFM can produce fused image that has good spatial and spectral fidelity to the reference image, which means it has the potential to generate synthetic data to support the studies that require high STSR satellite imagery.

Keywords: Hybrid spatial-temporal-spectral fusion, high resolution synthetic imagery, least square regression, sparse representation, spectral transformation.

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Authors: Young-Hwan Song, Hyung-Jun Kwon, Myung-Jin Bae

Abstract:

As the remedy used music becomes active and meditation effect through the music is verified, people take a growing interest about psychological balance or remedy given by music. From traditional studies, it is verified that the music of which spectral envelop varies approximately as 1/f (f is frequency) down to a frequency of low frequency bandwidth gives psychological balance. In this paper, we researched signal properties of music which gives psychological balance. In order to find this, we derived the property from voice. Music composed by voice shows large value in NCSD. We confirmed the degree of deference between music by curvature of normalized cumulative spectral distribution. In the music that gives psychological balance, the curvature shows high value, otherwise, the curvature shows low value.

Keywords: Cognitive Psychology, Normalized Cumulative Spectral Distribution, Curvature.

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Authors: Akrem Sellami, Imed Riadh Farah, Basel Solaiman

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With the development of HyperSpectral Imagery (HSI) technology, the spectral resolution of HSI became denser, which resulted in large number of spectral bands, high correlation between neighboring, and high data redundancy. However, the semantic interpretation is a challenging task for HSI analysis due to the high dimensionality and the high correlation of the different spectral bands. In fact, this work presents a dimensionality reduction approach that allows to overcome the different issues improving the semantic interpretation of HSI. Therefore, in order to preserve the spatial information, the Tensor Locality Preserving Projection (TLPP) has been applied to transform the original HSI. In the second step, knowledge has been extracted based on the adjacency graph to describe the different pixels. Based on the transformation matrix using TLPP, a weighted matrix has been constructed to rank the different spectral bands based on their contribution score. Thus, the relevant bands have been adaptively selected based on the weighted matrix. The performance of the presented approach has been validated by implementing several experiments, and the obtained results demonstrate the efficiency of this approach compared to various existing dimensionality reduction techniques. Also, according to the experimental results, we can conclude that this approach can adaptively select the relevant spectral improving the semantic interpretation of HSI.

Keywords: Band selection, dimensionality reduction, feature extraction, hyperspectral imagery, semantic interpretation.

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Authors: Hamioud Saida, Khalfallah Salah

Abstract:

In this study, a spectral element method (SEM) is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.

Keywords: Elastically supported Euler-Bernoulli beam, free-vibration, spectral element method, Winkler foundation.

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Authors: R. Sabre, W. Horrigue, J. C. Simon

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This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: Spectral density, stable processes, aliasing, periodogram.

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Authors: A. Benyahia, M. Zergoug, M. Amir, M. Fodil

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The main objective of this work is to enhance the Pulsed Eddy Current (PEC) response from the aluminum structure using signal processing. Cracks and metal loss in different structures cause changes in PEC response measurements. In this paper, time-frequency analysis is used to represent PEC response, which generates a large quantity of data and reduce the noise due to measurement. Power Spectral Density (PSD) after Wavelet Decomposition (PSD-WD) is proposed for defect detection. The experimental results demonstrate that the cracks in the surface can be extracted satisfactorily by the proposed methods. The validity of the proposed method is discussed.

Keywords: NDT, pulsed eddy current, continuous wavelet transform, Mexican hat wavelet mother, defect detection, power spectral density.

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Authors: Keigo Matsuura, Isao Tomita

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We have studied a method to widen the spectrum of optical pulses that pass through an InGaAsP waveguide for application to broadband optical communication. In particular, we have investigated the competitive effect between spectral broadening arising from nonlinear refraction (optical Kerr effect) and shrinking due to two photon absorption in the InGaAsP waveguide with χ(3) nonlinearity. The shrunk spectrum recovers broadening by the enhancement effect of the nonlinear refractive index near the bandgap of InGaAsP with a bandgap wavelength of 1490 nm. The broadened spectral width at around 1525 nm (196.7 THz) becomes 10.7 times wider than that at around 1560 nm (192.3 THz) without the enhancement effect, where amplified optical pulses with a pulse width of ∼ 2 ps and a peak power of 10 W propagate through a 1-cm-long InGaAsP waveguide with a cross-section of 4 (μm)2.

Keywords: InGaAsP Waveguide, χ(3) Nonlinearity, Spectral Broadening.

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Authors: Zhenyu Zhao, Lei You

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The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Do Phuc, Nguyen Thi Kim Phung

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In this paper, we represent protein structure by using graph. A protein structure database will become a graph database. Each graph is represented by a spectral vector. We use Jacobi rotation algorithm to calculate the eigenvalues of the normalized Laplacian representation of adjacency matrix of graph. To measure the similarity between two graphs, we calculate the Euclidean distance between two graph spectral vectors. To cluster the graphs, we use M-tree with the Euclidean distance to cluster spectral vectors. Besides, M-tree can be used for graph searching in graph database. Our proposal method was tested with graph database of 100 graphs representing 100 protein structures downloaded from Protein Data Bank (PDB) and we compare the result with the SCOP hierarchical structure.

Keywords: Eigenvalues, m-tree, graph database, protein structure, spectra graph theory.

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